Method and system for assessing quality of spot welds

ABSTRACT

A system and method for assessing the quality of spot weld joints between pieces of metal includes an ultrasound transducer probing a spot weld joint. The ultrasound transducer transmits ultrasonic radiation into the spot weld joint, receives corresponding echoes, and transforms the echoes into electrical signals. An image reconstructor connected to the ultrasound transducer transforms the electrical signals into numerical data representing an ultrasound image. A neural network connected to the image reconstructor analyzes the numerical data and an output system presents information representing the quality of the spot weld joint. The system is trained to assess the quality of spot weld joints by scanning a spot weld joint with an ultrasound transducer to produce the data set representing the joint; then physically deconstructing the joint to assess the joint quality.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/359,280, filed on Feb. 20, 2002; and U.S. ProvisionalApplication No. 60/359,275, filed on Feb. 20, 2002. The disclosures ofthe above applications are incorporated herein by reference.

FIELD OF THE INVENTION

[0002] The present invention relates generally to a method and systemfor assessing the quality of spot welds and, more particularly, anon-destructive method and system for assessing the quality of spotwelds according to measured acoustic parameters.

BACKGROUND OF THE INVENTION

[0003] Sheet metal joining processes are widely used in many industries,such as the aerospace and automotive industries. Among these processes,resistance spot welding is the most common procedure used to join metalsheets because it has high process speed and is easily adopted in massproduction lines. As these industries grow, the quality control of spotwelds becomes an important issue for manufacturers eager to improvetheir output capacity and product quality.

[0004] The quality of the spot weld is affected by welding processes andthe design of the joint. Many factors have to be taken into account,such as metallurgic reactions, thermal behaviors, chemical composition,condition of the base metal, welding conditions, and the weldingequipment. Furthermore, the intricate relationship between these factorsmakes it more difficult to control the quality of spot welds. Numerousefforts have been made to improve weld quality through differentapproaches; nevertheless, most of them are not overall solutions due tothe lack of adequate equipment and efficient algorithms to inspect theseimprovements.

[0005] The conventional strategy for spot weld quality controlinspection usually consists of a weld current-resistance monitoringsystem to maintain consistent welding parameters, and an after weld,spot weld examination process, according to a standard set up by theAmerican Welding Society for a particular industry. The spot weldexamination standard typically includes visual inspection of the weldsurface and destructive testing of collected weldment. To determine weldquality, visual inspection of the surface appearance and weld size areimportant indicators. Other important indicators, by destructiveinspection, are weld size, penetration, strength, ductility, internaldiscontinuities, and sheet separation and expulsion. Weld consistency,assessed by monitoring welding parameters, is another importantindicator. But these weld quality indicators are vague due to theinsufficient quantified description. To apply these specifications inpractical manufacturing cases, the indicators must be converted toquantified inspection standards. The Welding Handbook and the ResistanceWelding Manual do indeed quantify these indicators, but even then spotweld quality control relies mainly on an on-line supervising unit tomonitor welding parameters, on-line inspectors to perform visualinspection, and statistical sampling techniques for off-line destructivetesting.

[0006] More importantly, the weld quality indicators are mostly forvisual inspection and destructive testing, which are typicallyseparately conducted. Thus, present weld quality control does not takeinto account the combined effect of those indicators. Furthermore, thetrue quality of the spot weld, i.e., its strength, is only presumed byoff-line destructive sample tests. Unless every spot weld is examined,there is no certainty that the required strength has been met.

[0007] Acoustic methods are a commonly used non-destructive testingmethod that has been used for various inspection applications. Unlikeother non-destructive testing methods, the acoustic method provides bothsurface and internal information. Moreover, the acoustic method allowsdeeper penetration into specimens and higher sensitivity to smalldiscontinuities. Acoustic methods, however, are not flawless. The mostsignificant limitations include the requirements of a propagatingmedium, or couplant fluid, which is required for acoustic wavepropagation between the acoustic probe and the test specimen, andskillful operators for operating the devices and analyzing the acousticinformation.

[0008] While the first limitation is typically overcome because thematerials for joining in the automotive and aerospace industries areusually galvanized or coated and thus will not be damaged by anycouplant fluid, the second limitation—the need for skillful operators—ismuch more significant. The on-line inspection of spot welds is verydifficult because it is not economical to train every worker in theplant to be a tester/analyzer/operator.

[0009] More importantly, the acoustic method, by its very nature, limitsthe practicality of an on-line inspection. The acoustic method, unlikethe optical or x-ray method that receives two-dimensional informationthrough one process, has to go through point-to-point scanningprocedures to obtain two-dimensional information. There are several waysto display acoustic information, and they can be categorized by theinformation obtained. The most common ones are A-, B-, and C-scans thatcan be selected to show the internal defects as required.

[0010] The A-scan, the simplest presentation, and widely used isconventional ultrasonic NDE devices, shows the amplitude of the echoes,or the reflection, as a function of time at a selected point on the worksurface. The duration of time between different peaks represents thetime needed for acoustic waves to travel between discontinuities.

[0011] The B-scan follows the same procedure as the A-scan, but repeatsthe signal-catching procedures while the probe scans along the straightline on the surface. Thus, an image of the cross-section of a componentis built up. The measured amplitude is displayed as a colored dot on themonitor and its coordinant is defined by the position of the probe(X-coordinate) and the traveling time (Y-coordinate) of the acousticpulse.

[0012] If the amplitude of a particular echo is monitored at each pointon a certain depth of the workpiece, a C-scan can be performed.Measurements at each point are taken using two-dimensional scanning andelectronic gate mechanisms that produce the plan for the level of thedefect. This scan only gives the information at the preset depth of theelectronic gate. While the C-scan provides the richest information, andis therefore more desirable for quality control purposes, it is also themost time consuming scan, and therefore difficult to perform on-line.

[0013] Conventional quality control devices for spot welding cannotperform on-line inspection of spot welds, nor can they provide feedbackto the welding control system. In this way, the traditional qualitycontrol systems are similar to statistical welding parameter monitoringsystems. While it is imperative to combine the idea of on-line qualityinspection with closed-loop feedback control in a robust spot-weldingcontrol system, there is not an acoustic method capable of manipulatingreal-time control and on-line quality inspection.

SUMMARY OF THE INVENTION

[0014] A novel acoustic method and system provides real-time scanningfor on-line quality inspection of spot welds. The method and systemallows a large amount of acoustic information to be retrieved,processed, and presented in a short period of time to facilitateon-line, non-destructive inspection of spot welds employing intelligentcontrol software and state-of-the-art hardware. This intelligent systemfor on-line, real-time, non-destructive inspection of spot welds employsnovel algorithms for analyzing the information acquired by an acousticdevice, and is capable of providing go/no-go responses to on-lineworkers in a real-time fashion. Furthermore, feedback can be provided tothe welding control unit during the inspection process.

[0015] The method and system for spot weld quality assessment correlatesthe quality of spot welds with acoustical parameters built bystatistical and neural network methods. The statistical and neuralnetwork methods provide precise predictions for assessing weld qualityand allow the on-line inspection of spot weld quality in real time. Themethod and apparatus for acoustic inspection detects any inconsistentweld strength, and provides feedback to the welding unit, wherebydesigners are able to reduce the total number of spot welds and reducemanufacturing costs.

[0016] The invention overcomes the limitations of the acoustic imagingand provides a closed-loop feedback quality-advisor method and system.Once the acoustic inspection system detects defects or inconsistent weldstrength, the system provides more accurate feedback to the welding unitthan traditional current/resistance monitoring. Further, the system andmethod according to the invention are able to provide on-line feedbackof the weld quality and to perform inspections based on the internalstructure of the welds, both features that the traditionalcurrent/resistance monitoring system were not able to provide. Further,the apparatus and method according to the invention compliment thedesign process because the integrity of any given weld can be predictedbased on the acoustic information, which helps designers reduce thetotal number of spot welds and thereby reduces the manufacturing costs.

[0017] Further areas of applicability of the present invention willbecome apparent from the detailed description provided hereinafter. Itshould be understood however that the detailed description and specificexamples, while indicating preferred embodiments of the invention, areintended for purposes of illustration only, because various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

[0019]FIG. 1 is a schematic illustrating an acoustic microscope systemin accordance with a preferred embodiment of the present invention;

[0020]FIG. 2 is a flow chart for a method of analyzing and qualifyingspot weld joints in accordance with a preferred embodiment of thepresent invention;

[0021]FIG. 3 is a more detailed schematic illustrating an acousticimaging system in accordance with a preferred embodiment of the presentinvention;

[0022]FIG. 4 is a diagram of a theoretical temperature distribution in aspot weld nugget;

[0023]FIG. 5 is a diagram of an experimental temperature distribution ina spot weld nugget;

[0024]FIG. 6 is a diagram of a nugget structure in a spot weld;

[0025]FIG. 7 is a graphical representation of the steps of a method ofanalyzing and qualifying spot weld joints in accordance with a preferredembodiment of the present invention;

[0026]FIG. 8 is a table including the mathematical representations ofdilation and erosion in accordance with a preferred embodiment of thepresent invention;

[0027]FIG. 9 is an abstract model of a neuron;

[0028]FIG. 10 is a multi-layer feed-forward neural network in accordancewith a preferred embodiment of the present invention;

[0029]FIG. 11 is a table including weld quality criteria in accordancewith a preferred embodiment of the present invention;

[0030]FIGS. 12 and 13 are tables summarizing exemplary experimentalresults in accordance with a preferred embodiment of the presentinvention;

[0031] FIGS. 14-16 are graphical representations of exemplaryexperimental results in accordance with a preferred embodiment of thepresent invention;

[0032]FIGS. 17 and 18 are tables summarizing exemplary experimentalresults in accordance with a preferred embodiment of the presentinvention;

[0033]FIG. 19 is a graphical representation of exemplary experimentalresults in accordance with a preferred embodiment of the presentinvention;

[0034]FIGS. 20 and 21 are tables including coefficients of linear andnonlinear models in accordance with a preferred embodiment of thepresent invention; and

[0035]FIGS. 22 and 23 are graphical representations of exemplaryexperimental results in accordance with a preferred embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0036] The method and apparatus for assessing the quality of spot weldsemploys a rapid and robust algorithm for an acoustic or imaging systems.An acoustic microscope system such as one described in U.S. patentapplication Ser. No. 09/283,397, filed Apr. 1, 1999 and herebyincorporated by reference, is shown schematically in FIG. 1. Thesoftware and algorithms according to the invention rapidly analyze theinformation acquired by the acoustic device, and provide a go/no-goresponse to on-line workers in a real-time fashion. Optionally, feedbackcan be provided to a welding control unit during the inspection process.

[0037] Acoustic Wave Propagation Through A Weld Nugget

[0038] The spot weld nugget is an anisotropic material withmicrostructures different from its base metal. With reference to FIG. 2,the study of acoustic wave propagation in the weld nugget includesmetallurgical analysis and characterization of the mechanical andphysical properties of weld nuggets, including dendrite structures andferrous areas. Further, the propagation and the interaction of focusedacoustic beams inside the spot welds are also analyzed. From thisanalysis and characterization, the connection between weld nuggetstructures and the associated acoustic images are understood.

[0039] The relationship between the acoustic information in spot weldsand the quality of spot welds is learned through the study of theacoustic images, including information such as the profile of surfaces,shape and size of weld nuggets, and size of defects. After quantifyingthis information, it is formulated as a quality index of spot welds,whereby the acoustic image can be analyzed to extract the desiredinformation. In order to quantify and analyze this information, thefollowing three steps must be performed: First, mathematical morphologyis used to improve the acoustic images by eliminating noise, improvinggeometrical shape, and reshaping important objects inside the spot weld.Such morphology techniques such as dilation and erosion allow porosityto be grouped geometrically and permit the joint effect of groupporosity to be studied. Second, segmentation using a thresholdingtechnique to distinguish desirable objects from noise, whereby the mostimportant information is left for analysis. The threshold that separatesthe peaks on a color/gray level histogram is selected based on knowledgegained from the mathematical morphology. Third, edge detection is usedto distinguish discontinuity information inside the nugget from thenugget area, and to build up clear and continuous boundaries for thoseobjects. After edge detection, the boundaries obtained in edge detectionare used to calculate the area of the desired information.

[0040] Spot weld quality indexes, for correlation with acoustic imageparameters, are established through destructive testing. These qualityindexes can include the strength of the weld, the nugget size, and aquality judgment based on an expert opinion.

[0041] The study of the parameters can be approached as a two stepprocess. First, the parameters are analyzed statistically, such asthrough an Analysis Of Variance (ANOVA) method. This contributes to theselection of significant parameters to build up the quality index forwelds. After the statistical analysis, a mathematical relationship isbuilt between the weld index and the quantified information. Second, therelationship between the weld quality and the screened parameters fromthe first step are established using artificial neural networks andnon-linear regression methods. The artificial neural network method isused to determine the weld index as a non-quantified good/bad judgment,and to establish the relationship between these non-quantified judgmentsand the quantified weld index information. The non-linear regressionmethod, targeted at simpler weld quality indicators (e.g., the size ofwelds), is used to build a mathematical relationship between the weldindices obtained in the first step and the quality indicator.

[0042] By importing the extracted knowledge into a control mechanism, aportable hand-held acoustic device according to the invention providesan intelligent mechanism for spot weld inspection. The qualityevaluation methods provide reliable results, the statistical methodprovides a nugget diameter predictor, and the neural network modeldetermines nugget integrity. Regardless of which model is adapted, theportable acoustic device serves as an on-line advisor for workers, andprovides closed loop feedback to a robot welding control system.

[0043] The method and apparatus according to the invention preferablyemploys an Acoustic Microscope (AM) 10, which has three-dimensionalimaging capability. With reference to FIG. 3, the AM 10 includes anacoustic pulse receiver 20 and generator 30. The pulse generator 30generates an electrical pulse, and the receiver 20 collects reflectedsignals. The acoustic wave generated can be a continuous pulse or ashort pulse, depending on the system requirements. In the case of matrixarray probe, The SAM 10 is connected to an acoustic probe 50 by amultiplexor 40. The acoustic probe 50 includes a planar focus matrixarray transducer. Most transducers use a piezomaterial element with anoptical quality ground lens to provide the desired quality of acousticbeam alignment and focusing. As a contact with sample used eithercoupling liquid or polystyrene delay. The material of the acoustic lensshould have low attenuation and high velocity to minimize aberrations.The probes are designed for operation with the acoustic beam intovarious frequencies from 5 MHz to 2 GHz. The transducer convertselectric pulses into mechanical vibrations or vice versa.

[0044] The precision of the acoustic beam focus primarily depends onspherical aberration; consequently, the spherical aberration itselfdepends on the ratio of the ultrasound propagation velocities in liquidand the velocities inside the sound-guide in the transducer. The AM 10uses a coupling fluid, which provides the acoustic waves a medium tosupport their propagation. Between the acoustic probe 50 and a testspecimen 100, the medium must be a fluid to allow the scanningprocedure. Two major concerns in choosing a couplant fluid are thefluid's attenuation to acoustic waves and its applicability to the testspecimen. The performance varies under different coupling fluids anddifferent temperatures. Of all the coupling fluids, water, ultrasoundgel and ethanol are the most preferred.

[0045] The AM 10 is a computer-controlled ultrasonic scanning systemdesigned for examining the detailed internal structure of a wide rangeof parts. An AM 10 generally includes: a piezoelectric transducer togenerate a high radio frequency acoustical pulse and an acoustic probe,both components included in the acoustic probe 50, with a liquidcoupling medium for the pulse to propagate through; an electronic ormechanical scanning system 60 that can relate to the desired region inreliable steps; a memory unit 70 to store the achieved signal step bystep; an analog to digital converter 80 to transfer signals to images;and a monitor to display images 90.

[0046] The performance of the AM 10 depends on the frequency of theultrasound wave, type of transducer, the nature of the immersion medium,and the properties of the investigating materials. The nature of thefrequency of ultrasound affects the resolution of microscopic imagingand the depth of penetration, but in a contrary way. A higher frequencyof ultrasound offers a better resolution microscopic image, butshallower penetration of the testing samples. Thus, to choose a properfrequency of ultrasound for a particular testing example requires acompromise between the resolving power and the degree of penetration.

[0047] The microstructure of the nugget region of a spot weld isconsidered an anisotropic region. In order to assess spot weld quality,it is crucial to formulate the phenomenon of acoustic wave propagationin anisotropic materials. When a weld is deposited, the first grains tosolidify are nucleated by the unmelted base metal, and the orientationof crystal grains is in the same direction toward the steepesttemperature gradient. While solidifying, metals grow more rapidly incertain crystallographic directions, and the direction of crystal growthis perpendicular to the isotherms. Hence, favorably oriented grains growfaster for substantial distances, while the faster growing grains blockthe growth of others in a non-favorable orientation. The aforementionedfavorable crystallographic direction is the [100] direction in cubiccrystals, such as body central cubic or face central cubic. The [100]direction is the least closely packed direction in cubic crystals. The[100] crystals' growth directions and the direction of the steepesttemperature gradient are the same in a spot weld because there is nowelding speed involved.

[0048] Because of the crystals' growth directions, weld pools solidifyin a cellular or dendritic growth mode depending on the composition andsolidification rates. Both modes cause micro-segregation of alloyingelements. As a result, the weld metal may be less homogeneous than thebase metal. During the welding solidification, three stages ofmicrostructure formulations can be found. In the first stage, epitaxialgrowth from the base metal is likely to occur initially in the planargrowth front because the temperature differences inside a weld rangehave an extensive range. In the second stage, during further cooling,the temperature gradient decreases, resulting in a planar to cellularmicrostructure transition. In the third stage, when the temperaturegradient further changes, the primary cellular microstructures becomeunstable and develop secondary arms called dendritic structure.

C₁₁=λ

[0049] Analysis of Wave Propagation in the Nugget of a Spot Weld

[0050] Having reviewed wave propagation in an isotropic material and aprimitive anisotropic material, wave propagation in the nugget of a spotweld, which is a hexagonal symmetric case with five elastic constants,will now be described. The spot weld nugget is an irregularly shapedartifact with rough surfaces on both sides, and its metallurgicalstructure is different from the original sheet metal. Moreover, theexistence of discontinuities, porosity, and inclusion inside the weldnugget makes the acoustic wave propagation more difficult to study. Thesolidification processes in welds affect the crystallographicorientation. The direction of the grain growth follows the steepesttemperature gradient, and the crystal growth direction is the [100]direction of the cubic crystal. Thus, for a spot weld, the examiningacoustic waves are going through the [100] direction of the dendriticcrystals. FIGS. 4 and 5 demonstrate the temperature distribution in boththeoretical and experimental analysis. FIG. 6 shows the possible crystalgrowth direction in the spot weld nugget, which will be on the equiaxedgrain.

[0051] Because acoustic waves propagate through the [100] direction ofthe spot weld nugget in the core of the nugget, we can substitute thedirection unit into the above equation as l=1, m=0, and n=0. We canderive a simplified wave propagation model as:

λ₁₁C₁₁

λ₂₂=λ₃₃C₄₄

[0052] Solving the eigenvalue problem, then:

(C ₁₁ −ρC ²)(C ₄₄ −ρC ²)=0

[0053] The wave speeds are:$C_{L} = {{\sqrt{\frac{C_{11}}{\rho}}C_{SH}} = {C_{SV} = \sqrt{\frac{C_{44}}{\rho}}}}$

[0054] The longitudinal wave speed and the direction calculated here isproven to be correct in Kupperman, D. S., Reimann, K. J., “UltrasonicWave Propagation and Anisotropy in Austenitic Stainless Steel WeldMetal”, IEEE Transactions on Sonics and Ultrasonics, Vol. SU-27, No. 1,pp. 7-15, 1980, hereby incorporated by reference in its entirety.However, the shear waves traveling across the dendrites region with thepolarization direction parallel to the dendrites will have a differentattenuation pattern compared to the shear waves propagating in otherdirections.

[0055] The dendrites in spot weld nuggets are long, cylindrical singlecrystals with orientation in the vertical [100] direction. Assuming thedendrite's cylindrical crystal is symmetric about the Z-axis, as shownin FIG. 6, the general orthorhombic symmetry object can be reduced to behexagonally symmetrical. The independent elastic constants are reducedfrom nine (9) to five (5) according to Kupperman and Reimann's study.The five independent elastic constants can be calculated by the modifiedformula as:${\overset{\_}{C}}_{11D} = {{\overset{\_}{C}}_{22D} = {{\overset{\_}{C}}_{11} + \frac{3\gamma \quad C}{20}}}$${\overset{\_}{C}}_{33D} = {{\overset{\_}{C}}_{11} + \frac{2\gamma \quad C}{5}}$${\overset{\_}{C}}_{44D} = {{\overset{\_}{C}}_{55D} = {{\overset{\_}{C}}_{44} - \frac{\gamma \quad C}{5}}}$${\overset{\_}{C}}_{66D} = {{\overset{\_}{C}}_{44} + \frac{\gamma \quad C}{20}}$${\overset{\_}{C}}_{13D} = {{\overset{\_}{C}}_{23D} = {{\overset{\_}{C}}_{12} - \frac{\gamma \quad C}{5}}}$${\overset{\_}{C}}_{12D} = {{\overset{\_}{C}}_{12} + \frac{\gamma \quad C}{20}}$

[0056] where λ is the texture anisotropy factor and C can be calculatedas: C=C₁₁-C₁₂-2C₄₄. Detailed description can be found in Dewey, B. R.,et al, “Measurement of Ansiotropic Elastic Constants of Type 308Stainless-Steel Electroslag Welds”, Experimental Mechanics, Vol. 17, No.11, pp. 420-26, 1997, and Ekis, J. W., “Ultrasound Examination forResistance Spot Welds of Filter Connectors”, Materials Evaluation, Vol.52, pp. 462-63, 1994, hereby incorporated by reference in its entirety.

[0057] There are two ways to calculate the elastic constants for thespot-weld type of anisotropy. The first one is to use static tensiletesting and the second one is to use acoustic testing. According to thefirst method, samples cut in three principal local directions arefabricated. Tensile tests are then applied at different directioncosines. The longitudinal elongation and the laterial contraction arethen measured. Finally, a strain-stress relationship is used tocalculate the components of the stiffness matrix.

[0058] The second method, the acoustic testing method, starts with afresh cut sample to allow precise directional measurement. Then theacoustical velocity is measured relative to a certain locally preferredsolidification direction. Following this, the method continues withanother fresh cut sample. The acoustical velocity is measured relativeto another preferred solidification direction. When the directionalacoustical velocities have been recorded, the elastic stiffness matrixcan be obtained by the Christoffel equation. Details of these procedurescan be found in the study of Dewey et al.

[0059] Because the grain growth in the weld nugget is in the [100]direction in the core region, the behaviors of the acoustic waves can beanticipated. However, in other regions of the weld nugget, themicrostructures of equiaxed grain growth make the prediction of acousticwave behaviors difficult. Due to the irregular shape of the nugget, themicrostructures in non-core regions of the weld nuggets are equiaxed yetrandomly arranged. This affects the pattern of acoustic wavepropagation, for example, by misguiding the acoustic waves and returnbias signals. The other major factor affecting acoustic wave propagationis the HAZ of the weld. The HAZ has usually been recrystallized and itsmicrostructures have been changed, which results in a re-focusing of theacoustic beam and therefore misinterpretation. Furthermore, the meltedcoating material will produce contact between the base metals and allowthe acoustic waves to pass through. This may change the results of theanalysis of the weld nuggets. In some cases, a deep indentation of weldnuggets can re-focus the acoustic beam and produce signal-free regions.

[0060] The irregular shape of the nugget raises an interpretationproblem for the acoustic method mathematically. An experimental model topredict spot weld quality based on its acoustic information is to beestablished. By correlating the acoustic parameters and the results fromexperiments, a reliable index of weld quality can be established.

[0061] The results of acoustic image analysis are sets of pixel-basedpictures with abundant information that allows us to scrutinize thedetail of every aspect of the metallurgical and acoustic properties ofeach spot weld in the study. The acoustic microscopy method can providethe information about quality of spot weld nuggets by examining thenon-homogeneous objects inside nuggets such as: bubbles, inclusions,explosive welds, and porosity. The non-homogeneous objects inside, andthe surface indentation, guide the acoustic waves and provide apseudo-acoustic-image for welded nuggets.

[0062] There are two different types of studies performed for thevalidity test of the acoustic method. The first one is to verify theresults of the acoustic method by using another non-destructive method.The second one is to test the ability of the acoustic method bydescribing the detection of artifact defects. In the first test, thecommonly used optical examination procedure is employed as the tool forverifying the result of the acoustic test. The advantages of an acoustictest is that it permits internal examination of structure, but has thedisadvantage that the measurement results need to be calibrated. Theoptical test has the advantage that it allows visual inspection ofnugget size but only surface information is obtained.

[0063] This approach is aimed at the calibration between the opticalmethod and the acoustic microscope method. Instead of peeling the spotweld samples, this approach works on “peeling nuggets.” The proceduresof this approach will be described as follows:

[0064] 1. Cut and grind the welding coupons to nugget tablets.

[0065] 2. Polish these samples from a selected side.

[0066] 3. Perform acoustic inspection of spot weld samples from bothsides.

[0067] 4. Examine the peeled nuggets from the selected side by theoptical method. Examine the peeled nugget from both sides by theacoustic method. The acoustic signal windows should be set close to theselected side of the nugget. This step will help to examine thecorrelation between the acoustic method and the optical method.

[0068] 5. Peel the nugget into thinner tables, and repeat steps 2through 4.

[0069] 6. Continue peeling the nugget until the desired thickness hasbeen reached.

[0070] 7. Calibrate the results from the optical method and the acousticmicroscope method.

[0071] Verification Results of the Non-Destructive Method.

[0072] Three types of welds, categorized by their stack up, wereexamined to verify results: Type 1 (0.03″ stack on 0.045″), Type 2(0.04″ stack on 0.06″) and Type 3 (0.06″ stack on 0.07″). Two welds ofdifferent welding parameters were produced on Type 1, and two and fourwelds on Types 2 and 3, respectively. For Type 1 and Type 2, theacoustic estimation of the nugget diameter typically closelyapproximates the diameter determined by the optical method. For Type 3,with thicker base metals which need a longer heating process duringwelding, the HAZ region is larger than Type 1 and 2. The HAZ affects themicrostructures while recrystallization substantially affects bothnon-destructive tests. For optical examination, the HAZ reacts to theetching process, and produces larger images. In comparison, aring-shaped region is observed by the acoustic method.

[0073] Acoustic Image Study

[0074] With reference to FIG. 7, to study the acoustic image, fourpractical steps are employed to convert the information into quantitiesfor further studies. First, mathematical morphology is used tocharacterize geometric structure by numerical value. This method isusually used prior to image recognition and pattern identification toimprove the geometric shapes of objects inside an image for furtherstudy. The purpose of the process is to filter out information notrelated to objects.

[0075] The operations of morphology are dilation, erosion, opening andclosing. The effect of the dilation operator on an image is to enlargethe boundaries of selected objects. The effect of the erosion operatoron an image is to erode the boundaries of selected objects. The openingoperation includes performing erosion followed by dilation. The closingoperation includes performing dilation followed by erosion. Dilation anderosion operators are used to emphasize the discontinuities insidenuggets. The definition of dilation and erosion operations and theirmathematical representation is listed in FIG. 8.

[0076] After the acoustic images have been readied for furtherexamination by morphological processes, the thresholding method is usedto separate out the interesting objects inside welds, such as weldnugget size, nugget shape, porosity, and inclusion. This algorithmconverts a multi-gray-level image into an image containing fewergray-level values. The operation defined for three gray-level regionsfor separating noise of image, nugget area, and discontinuities insidenuggets is: ${g\left( {x,y} \right)} = \begin{Bmatrix}{{{G_{2}\quad {if}\quad {f\left( {x,y} \right)}}\rangle}T_{2}} \\{{G_{1}\quad {if}\quad T_{1}} \leq {{f\left( {x,y} \right)}{\langle T_{2}}}} \\{{G_{0}\quad {if}\quad {f\left( {x,y} \right)}} \leq T_{1}}\end{Bmatrix}$

[0077] where f(x,y) represents the original image; g(x,y) is the imageafter thresholding; T₁ and T₂ are thresholding values; and G₀, G₁ and G₂are the values of gray-level.

[0078] After thresholding, edge detection is performed. This processhelps separate objects in acoustic images. The edges of objects aredistinguished by the discontinuities or abrupt changes in gray-levelintensities. Since the gray-level numbers have already been reducedduring thresholding, the edges between objects inside the weld nuggetare quite clear.

[0079] Several other data processing techniques can be used to furtherenhance the ultrasonic images. These techniques include usage ofweighted calculations for ultrasonic signal processing, tiltcompensation, surface peak calibration, and time-of flight compensation.

[0080] Usage of weighted calculations allows distinguishing poormeasurement conditions from good ones. For example, when the transduceris not in a contact with the sample or the surface condition does notallow getting correct measurements, the algorithm will indicate that themeasurement is impossible. While standard methods would normally producea result in any case, it would appear completely inconsistent withreality. For example, in the case of a spot weld, this could lead to theerroneous detection of a normal weld when the weld is in factundersized.

[0081] This functionality is achieved with weights, which specify thedegree of reliability of the data. Critical data items are accompaniedwith this additional weight parameter. Ranging from 0 up to 100%, itspecifies the degree of reliability of the data stored in acorresponding item. There are several stages in the data processingpipeline that might change the weight(s) associated with the processeddata; mainly weights associated with different transducer elements(different A-scans) are updated during the surface peak detection, basedon its signal-to-noise ratio. If the surface peak is indistinct (itsamplitude is close to the noise level), the algorithm may reject thechannel from further consideration by attributing zero to thecorresponding weight. On the contrary, peaks with normal amplitudes aresubjected to following data processing stages with 100% weights. A-scanshaving indistinct peaks are marked with intermediate weight valuesranging from 0% up to 100%.

[0082] In the case of the spot-weld measurement, interpretation of thefinal result (the nugget diameter) is quite straightforward. Forexample, if it has 95% weight, it means that the measurement is likelyto be consistent; on the contrary, the low weight of the final resultwould indicate that the device most likely could not measure the nuggetsize and the operator has to repeat the measurement.

[0083] The tilt compensation method reduces the angular dependence forsmall, unfocused elements of the matrix transducer. After the algorithmhas found the positions and amplitudes of the surface peaks, it measuresa global tilt of the surface sample with respect to the transducersurface, which is approximated as a plane. This is done with weightedbilinear regression. Using the empiric tilt-amplitude calibration curve,it computes a factor to compensate the amplitude drop due to the tilt.The value of each sample point in each A-scan is multiplied by thatfactor. This calibration factor is a global value, and is applied forall transducer channels. This allows receiving C-scans with more stableamplitudes that are less dependent on the transducer tilt. Thecalibration curve is built as a result of a series of measurements onflat-parallel sheets of metal, mapping the amplitude of the signalreceived from the back face of the sheet.

[0084] Surface Peak Amplitude Calibration is a calibration method thatworks under assumption that a sample consists of a uniform material. Foreach transducer channel, it calculates an amplitude multiplicationfactor that depends on the amplitude of the surface peak. The factor iscalculated so that after multiplication, the amplitude of surface peaksare the same for all channels. This calibration method partiallycompensates for variations of amplitudes due to local surface conditions(i.e., topology variations).

[0085] Time-of-Flight (TOF) Compensation is useful since, due to a largedifference in the velocity of sound in immersion and in steel, directmapping of the time axis of an A-scan into the depth is impossible. Thesound travels through immersion much slower than it does in metal, andeach small variation in immersion thickness causes sufficientdisplacement of the following signals along the time axis. TOFcompensation involves shifting each A-scan along its time axis so thatthe position of surface peaks becomes the same for all channels. Thisensures that the C-scan is acquired from the specified depth rangerelative to the surface. An analogous effect may be achieved by varyingthe signal gates position according to the surface peak position. TheTOF compensation method stabilizes the range of depths from which thesignal is acquired.

[0086] Data Analysis

[0087] Analysis Method I: Statistical Correlation.

[0088] The acoustic imaging method provides abundant information afterimage extraction. However, this information consumes a major part of theprocessing resource and is computationally exhausting. Thus it isdesirable to limit the parameters that will be used in determining weldquality. In a preferred embodiment of the present invention, theparameters used include nugget diameter, depth of indentation, and areaof reflectors inside nuggets. The ideal quality identifier is thestrength of the weld nuggets. Quantity is difficult to measure and willvary from process to process. Consequently, a substitute quantity—thediameter measured from the destructive test (peel test)—is used foranalyzing the welding quality.

[0089] These quantity factors are determined as follows. First a groupof selected welding coupons is chosen. Next, a B-scan and C-scan imagesfrom the newly developed acoustic device is captured. A group ofparameters is selected according to existing knowledge. Destructivetests are conducted on these samples. The nugget diameters of the peeltest result are then measured. The ANOVA technique is used to screen outthe insignificant parameters. Finally, the nugget strength indicator isbuilt up by correlating significant parameters to the nugget diametersproduced by peel tests.

[0090] For a three variable system, α, β, and γare related to the nuggetdiameter S. The linear model will be:

S=C ₁ +C ₂ a+C ₃ β+C ₄γ

[0091] The polynomial model will be:

S=C ₁ +C ₂ α+C ₃ β+C ₄ γ+C ₅ αβ+C ₆ αγ+C ₇ βγ+C ₈ α ² +C ₉β² +C ₁₀γ²⁰

[0092] where Ci, i=1˜10 are constant coefficients.

[0093] After the formulation, an ANOVA table can be established toinvestigate the significance of these variables. Thus, some of theinsignificant parameters can be filtered out. The ANOVA provides theinferential procedure for testing the statistical hypothesis. One of theways to judge the significance of each variable is by assessing thecharacter of the F-score. A level of confidence for the significancetest can be set, for example, as either 95% or 99% to select thevariables which are to enter the next stage.

[0094] Either the linear multiple regression or the non-linear multipleregression method is then used to establish the constants associatedwith the acoustic parameters. A variety of commercial software existsfor solving non-linear regression. Most of them follow this procedure:an initial estimation for each variable is made and a curve defined bythe estimation is generated; the variables adjusted to fit the curvecloser to data points using algorithms such as the Marquardt method; thecurve is further adjusted to make it closer to the data set. Once thepre-set error limit is reached, the procedure is stopped and results arereported.

[0095] Through these procedures, a set of significant parameters aredetermined and their coefficients found. Consequently, the diameter ofthe weld will be predictable through the cumulative relationship, whichwill be an indicator of the spot weld quality.

[0096] Analysis Method II: Neural Networks.

[0097] To assess a spot weld by a general description such as agood/marginal/bad weld (instead of a more specific index, like bondingstrength) an artificial neural network (ANN) is used. This generaldescription is desirable as a criterion that can be easily adopted intoindustrial standards.

[0098] ANN were originally designed as a model to simulate how the humanbrain works. With reference to FIG. 9, the ANN is a simplified modelthat simulates human information passing behavior by artificial neurons.Each neuron has input and output which are related to the state of theneuron itself, a threshold function to decide on the input-outputrelationship, and unidirectional connection communication channels whichcarry numeric (as opposed to symbolic) data.

[0099] With reference to FIG. 10, the neural network model of thepresent invention is a three layer feed-forward model trained with thebackpropagation method with logistic function as the activationfunction. The logistic threshold function is:$\frac{1}{{f(x)} = {1 + ^{- x}}}$

[0100] where f (x) represents the output; and x is the input.

[0101] The back propagation method is desirable because it is easy toapply to a practical problem such as the problem examined. Thisalgorithm has been proven as very robust for training multiple layernetworks. It is also desirable because it is very effective when therelationship between input/output layers is nonlinear and the trainingdata is abundant.

[0102] According to a preferred embodiment of the present invention,there are/quantified parameters, j hidden units, and three output units(representing good/marginal/bad welds). W_(ij) stands for the weightbetween input layer i-th unit and j-th unit of the hidden layer. Theactivation function here has a special property such thatf(x)=f(x)(1−f(x)). The steps of the back propagation method of thepresent invention include:

[0103] 1. Computing the hidden layer neuron activation. The j-th hiddenlayer neural:$y_{j} = {f\left( {\left( {\sum\limits_{i}{x_{i}{{W_{1}\lbrack i\rbrack}\lbrack j\rbrack}}} \right) + \theta_{j}} \right)}$

[0104] 2. Computing the output layer neuron activation. The j-th outputlayer neural:

z _(j) =f((Σy ₁ W ₂ [i] [j])+τ_(j))

[0105] 3. Computing the output layer error, where the output differencesare equal to the desired values minus the computed values. For the i-thcomponent of error at the output layer:

e _(i) =z ₁(1−z ₁)(p ₁ −z ₁)

[0106] 4. Computing the hidden layer error. For the i-th component oferror at the hidden layer:$t_{1} = {{y_{1}\left( {1 - y_{1}} \right)}\left( {\sum\limits_{j}\quad {{{W_{2}\lbrack i\rbrack}\lbrack j\rbrack}e_{j}}} \right)}$

[0107] 5. Adjusting the weights for the second layer of the synapses.For the i-th neuron in the hidden layer and the j-th neuron in theoutput layer:

ΔW ₂

[i

j]=μy _(i) e _(j)

[0108] 6. Adjusting the weights for the first layer of the synapses. Forthe i-th neuron in the input layer and the j-th neuron in the hiddenlayer:

W ₁

[i

j]=λx _(i) t _(j)

[0109] Steps 1 though 6 are then repeated on successive training datauntil a specified value of output layer error is achieved. In the abovedescribed backpropagation equations, x, y, z are vectors for the outputneurons in the input layer, hidden layer, and output layer,respectively; W₁ and W₂ are weight matrices between the input-hiddenlayer and the hidden/output layer; p is the desired output vector; e andt are vectors for errors in the output and hidden layers; θ and τ arevectors of the threshold or bias value for the hidden layer and theoutput layer; and μ and λ are learning rate parameters for the hiddenlayer and the output layer.

[0110] The back propagation network has the ability to learn anyarbitrarily complex nonlinear mapping. With respect to the statisticsmethod, the proposed feed-forward method with one hidden layer is a veryclose projection pursuit regression.

[0111] In the preferred embodiment of the present invention, thesoftware acts as an analyzer with image processing tools. It performsneural network training and testing functions. Users can load images,perform basic image processing techniques, run default operations(thresholding/dilation/area calculation), prepare ANN training data,train ANN, prepare testing data, and test ANN results. In another modeof operation, the software, the software performs spot weld qualityexamination on pre-trained ANN.

EXAMPLES

[0112] The above system and methods will now be illustrated with severalexamples. These examples include examined specimens produced undercarefully controlled welding parameters (welding current, electrodepressure, and holding time) and identical metal conditions (e.g.,surface coating, thickness). Due to the continuous hardware improvement,weld specimens were separated into three groups chronologically. Thefirst group, with C-scan images as the results, was examined earlier byultra-Short Pulse Scanning reflection Acoustic Microscope (SPSAM). Thequality of these specimens was certified by experts from the best to theworst as setup, nominal, minimum, less than minimum, and stick weld,respectively. The minimum quality is the bottom line of an acceptedweld. The second group, with C-scan images as the results, was examinedby SPSAM as well. This group was peel tested and served as theverification group to test the Artificial Neural networks (ANN) modelbuilt by Group One. The specimens of Group Three were examined by boththe portable hand-held microscope and SPSAM.

[0113] Non-destructive acoustic tests were applied to specimens andacoustic information was recorded. Then destructive testing wasconducted on the second and third groups of specimens for conventionalnugget diameter measurement. Through destructive tests, the nugget sizeof each spot weld was found. This information was then integrated intothe results together with the parameters recognized by a methoddescribed below. The experimental procedures for the specimens arelisted in FIG. 11.

Example Group One

[0114] Two types of metal stack up were studied: Type I (0.03″×0.045″)and Type II (0.04″×0.06″). The criteria for identifying weld quality byexperts for each metal stack up is based on the size of the weld nugget.The criteria are listed in FIG. 12.

[0115]FIG. 13 lists exemplary results obtained by the acoustic imagemeasurement and analysis methods detailed above. These results involvethe quality indicator (e.g., setup, nominal, minimum, less than minimum,stick) and will be adopted in the ANN model developed for this study.Among these specimens, 120 samples including 24 setup, 24 nominal, 24minimum, 24 less than minimum, and 24 stick were chosen for each type ofstack up to train the ANN. The other 75 samples for each type were usedto test the neural networks model. In Type I stack up, all 75 samplesmatch the actual weld quality of the ANN corresponding model. For theType II stack up, 71 out of 75 samples match the weld quality of thecorresponding ANN model. The results indicate a coherent performance forthis model based on expert knowledge.

[0116] The results of Type II are plotted in FIGS. 14-16 according tothe selected acoustic parameters (area, maximum nugget diameter, andminimum nugget diameter). There exists no clear boundary between weldquality by considering a single parameter. For example, in FIG. 14, therange of “minimum” quality and “less than minimum” quality areoverlapped between 20 and 30. In other words, the quality of weld cannotbe decided by a single acoustic parameter.

Example Group Two

[0117] The following set of examples include one type of metal stack up(Type I, 0.03″×0.045″). This group of specimens is acoustically examinedand peel tested. The acoustic C-scan images are used to test thecorresponding ANN model built by the specimens of Group One. Theverification is 100% consistent to both (peel test and ANN) models. Theresults are listed in FIG. 17.

Example Group Three

[0118] In this set of examples, the three parameters chosen foranalyzing the weld quality are surface indentation, nugget diameter(measured from the acoustic method), and the total inclusion size insidethe nugget. The data of these parameters and the results from the peeltest are included in FIG. 18. The experimental result is normalized andplotted in FIG. 19 to provide visual assistance for choosing a properinterpretation of the weld quality.

[0119] There is no significant relationship between the normalized dataand the diameter measured from the peel test. The only parameter capableof portraying the relationship is the distance between the weldboundaries, the order of which cannot be decided since the coefficientof determination of the first and second order equations are so close.Therefore, both linear and nonlinear regression models are tested fordetermining the suitable model. The appropriate model is then used tocarry out the magnitude of the coefficients of the equation.

[0120] These three variable systems, α, β, and γ, which representindentation, acoustic diameter, and inclusion, respectively, are relatedto the diameter from peel test D. The linear model is:

D=C ₀ +C ₁ α+C ₂ β+C ₃γ

[0121] The polynomial model is:

D=C ₀ +C ₁ α+C ₂ β+C ₃ γ+C ₄ α ² +C ₅ β ² +C ₆ γ ² +C ₇ αβ+C ₈ βγ+C ₉αγ

[0122] where Ci, i=0˜9 are constant coefficients.

[0123] The coefficients of the linear and nonlinear regression modelsare shown in FIG. 20, and the results are plotted in FIG. 22 and FIG.23, respectively. FIG. 23 demonstrates that the polynomial model withten (10) constants is a closer prediction. The F-score of this model is170.36, which is substantially greater than the F-critical value of2.17. Therefore, this regression model is useful in predicting thediameters measured by the peel test. The sum of the residual square isreasonably small at 4.28.

[0124] To reduce the calculation efforts of this model, a t-test for thestatistical significance of each parameter is performed. Thesignificance level is chosen as 95%, and the t-value is 1.645, whichsuggests that some of the terms are insignificant. Hence the reducedequation can be rewritten as:

D=C ₀ +C ₁ α+C ₂ β+C ₃ α ² +C ₄ β ² +C ₅ γ ² +C ₆αβ

[0125] The coefficients are listed in FIG. 21.

[0126] The new model provides an explanation without losing much of thegenerality of the observed diameter with the coefficient ofdetermination equal to 0.969. The sum of the residual square is 5.755.

[0127] Through these procedures, a set of significant parameters isdetermined and their coefficients are retrieved. The peel diameter ofthe weld will be predictable through the cumulative relationship, whichwill be an indicator of spot weld quality.

[0128] The invention being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the invention, and all suchmodifications as would be obvious to one skilled in the art are intendedto be included within the scope of the following claims.

What is claimed is:
 1. A system for assessing the quality of a spot-weldjoint between pieces of metal, the system comprising: an ultrasoundtransducer for probing a spot-weld joint, the ultrasound transducertransmitting ultrasonic radiation into the spot-weld joint, receivingcorresponding echoes, and transforming the echoes into electricalsignals; an image reconstructor connected to the ultrasound transducerfor transforming the electrical signals into numerical data representingan ultrasound image; a neural network connected to the imagereconstructor for analyzing the numerical data; and an output system foroutputting information representing the quality of the spot weld joint.2. The system of claim 1, wherein the neural network comprises: an inputlayer including the numerical data representing the ultrasound image; ahidden neuron layer including a first weight matrix defining numericalrelationships between the numerical data representing the ultrasoundimage and an intermediate output; and an output layer including a secondweight matrix defining numerical relationships between the intermediateoutput and a final output.
 3. The system of claim 1, wherein the neuralnetwork comprises: an input layer having nodes for receiving input datarepresenting the ultrasound image; first weighted connections connectedto the nodes of the input layer, each of the first weighted connectionshaving a coefficient for weighting the input data; and an output layerhaving nodes connected to the first weighted connections, the outputlayer defining numerical relationships representing the quality of thespot weld joint.
 4. The system of claim 3, further comprising: a hiddenlayer having nodes connected to the first weighted connections, thehidden layer being interposed between the input and output layers; andsecond weighted connections connected to the hidden layer nodes and tothe output layer nodes, each of the second weighted connections having acoefficient for weighting the outputs of the hidden layer nodes.
 5. Amethod of training a computer system to assess the quality of spot weldjoints, the method comprising: scanning a first spot weld joint with adata acquisition device to produce a data set representing the joint;physically deconstructing the joint; assessing the joint quality; andaltering the structure of the computer system to elicit a futureresponse to stimuli based on a comparison of the joint quality to thejoint to the data set representing the joint.
 6. The method of claim 5,further comprising the step of repeating the above steps with at least asecond spot weld joint, wherein the computer system is altered to elicita future response to stimuli based on the results of all joint qualityand data set comparisons.
 7. The method of claim 6, wherein the steps ofaltering the structure of the computer system include altering at leastone weight matrix in a neural network.
 8. The method of claim 7, whereinthe step of altering the computer systems includes altering at least twoweight matrices using back propagation.
 9. The method of claim 8,wherein the step of back propagation includes the steps of: computing afirst layer neuron activation from a first layer neuron activationfunction, wherein the first layer neuron activation function defines amathematical relationship between the computer system input stimuli andan intermediate output data set, the mathematical relationship includinginformation from the first weight matrix; computing a second layerneuron activation from a second neuron activation function, wherein thesecond layer neuron activation function defines a mathematicalrelationship between the intermediate output and a final output dataset, the mathematical relationship including information from the secondweight matrix; computing a second layer error by comparing the finaloutput to a desired final output; computing a first layer error based onthe second layer error; adjusting the second weight matrix based on thesecond layer error; adjusting the first weight matrix based on the firstlayer error; and interactively repeating the above steps to reduce thesecond layer error.
 10. A method of analyzing an ultrasound image, themethod comprising the steps of: identifying critical data items;assigning each critical data item a weight parameter specifying thereliability of the data stored in a corresponding data item; performingsurface peak detection; and altering a weight parameter for a data itembased on the results of the surface peak detection to reflect a changein reliability.
 11. The method of claim 10, wherein the step of alteringthe weight parameter for the data item includes analyzing asignal-to-noise ratio determined by the surface peak detection.
 12. Themethod of claim 11, wherein the data items represent ultrasoundtransducer channels.
 13. The method of claim 12, further comprising thestep of rejecting a channel from further consideration based on thecorresponding weight parameter.
 14. A method of analyzing an A-scanultrasound image to reduce the angular dependence of matrix transducerelements and improve C-scan image quality, wherein the ultrasound imagerepresents a surface sample of a spot-weld joint, the method ofcomprising the steps of: locating the positions and amplitudes ofsurface peaks in the ultrasound image; measuring a global tilt of thesurface sample with respect to the transducer surface, using weightedbilinear regression; using an empiric tilt-amplitude calibration curveto compute an amplitude drop compensation factor based on the globaltilt; and multiplying the value of each sample point in each A-scan bythe amplitude drop compensation factor, such that the factor is appliedfor all transducer channels; wherein subsequently acquired C-scan imageshave more stable amplitudes that are less dependent on the transducertilt than images acquired using un-compensated transducers.
 15. Themethod of claim 14, further comprising the step of building thecalibration curve, wherein building the curve includes the steps of:using a series of measurements on flat-parallel sheets of metal; andmapping the amplitude of the signal received from the back face of thesheet.
 16. A method of compensating for variations in the velocity ofsound in different media in the analysis of ultrasound images, whereinan ultrasound transducer system is used to acquire ultrasound images,the method comprising the steps of: acquiring a set of A-scan ultrasoundimages; shifting each A-scan along its time axis so that the position ofsurface peaks becomes the same for all ultrasound transducer channels;and building a C-scan image from the A-scan images, wherein the C-scanimage reflects the compensation.